Silicon Piezoresistive Transducer Carrier Density Fundamentals and Gauge Factors
P-type silicon piezoresistors doped with boron to 1e18 cm-3 achieve an optimal balance between gauge factor magnitude and thermal coefficient stability.
Longitudinal Gauge Factor
Sensitivity Metric
Ratios of fractional resistance change to strain define how effectively a sensor detects forces parallel to current flow. The longitudinal gauge factor expresses this efficiency for resistors aligned exactly with the stress vector. Higher values indicate a more responsive device that can resolve smaller physical movements.
Lattice Alignment
Directional properties of the silicon crystal mean that the orientation of the resistor tracks relative to the axes is paramount. While the longitudinal gauge factor is typically high in the 110 direction, it drops significantly if the orientation is off by even a few degrees. Layout engineers orient the piezoresistors during mask design to capture the strongest signal possible.
Temperature Correction
Variability in atomic spacing modifies the interaction between charge carriers and the strained lattice. Because the longitudinal gauge factor decreases as thermal energy increases, compensation resistors are built into the same die to track these changes. Total measurement error is reduced when the electronics can apply real time correction to the incoming stream.
Performance Limit
Material constraints dictate the maximum obtainable signal before structural failure. Exceeding the linear range makes the longitudinal gauge factor appear to shift as the device enters a non linear region. Operational specs define the window within which the factor remains constant enough for high precision instrumentation.